Find $k$, if the line $4x-y=1$ is perpendicular to the line $5x-ky=2$.

If two lines with slopes $m_1$ and $m_2$ are perpendicular, the product of their slopes is $-1$:
$$m_1\cdot m_2=-1$$
For the first line $4x-y=1$:
$$y=4x-1⟹m_1=4$$
For the second line $5x-ky=2$:
$$ky=5x-2⟹y=\frac{5}{k}x-\frac{2}{k}⟹m_2=\frac{5}{k}$$
Since the lines are perpendicular:
$$4\cdot \left(\frac{5}{k}\right)=-1$$
$$\frac{20}{k}=-1$$
$$k=-20$$